1729.fsx

#r @"..\packages\FSharp.Charting.0.90.13\lib\net40\FSharp.Charting.dll"
#load "..\packages\FSharp.Charting.0.90.13\FSharp.Charting.fsx"



open System
open FSharp.Charting
open System.Windows.Forms
open System.Drawing


let posNum = seq {1..101}

let cube x = x * x * x 

let cubeposNum = 
    posNum 
    |> Seq.map (fun x -> (x, cube x))

let totalCombination = 
    cubeposNum 
    |> Seq.map (fun (a,b) -> cubeposNum |> Seq.map (fun (x,y) -> (a,x,b+y)))
    |> Seq.concat

let finalResult =
    totalCombination
    |> Seq.countBy (fun (x,y,z) -> z)
    |> Seq.filter (fun (x,y) -> y >= 4)
    |> Seq.map (fun (x,y) -> x)

let dirtyHack (inputSeq)=
    let a = inputSeq |> Seq.item 0
    let b = inputSeq |> Seq.item 1
    let c = inputSeq |> Seq.item 2
    (a, b, c)
 
let pairValues =
    finalResult 
    |> Seq.map (fun x -> totalCombination |> Seq.filter (fun (a,b,c) -> c = x ))
    |> Seq.map (fun a -> a |> Seq.map (fun (x,y,z) -> seq[x;y;z] |> Seq.sort |> dirtyHack))
    |> Seq.map (fun x -> x |> Seq.distinct)



//form crazyness - a copy paste from 2010 code :P

let form = new Form(Visible = true, Text = "A Simple F# Form",
                    TopMost = true, Size = Size(600,600))
 
let data = new DataGridView(Dock = DockStyle.Fill, Text = "Hardy–Ramanujan number",
                            Font = new Font("Lucida Console",12.0f),
                            ForeColor = Color.DarkBlue
                            )
 
 
form.Controls.Add(data)
 
data.DataSource <- (pairValues |> Seq.concat |> Seq.sortBy (fun (x,y,z) -> z) |> Seq.toArray)
data.Columns.[0].Width <- 200
data.Columns.[1].Width <- 200
data.Columns.[2].Width <- 200

data.Columns.[0].HeaderText <- "a"
data.Columns.[1].HeaderText <- "b"
data.Columns.[2].HeaderText <- "(a^3 + b^3)"


//Charting

let taxicabnumbers = pairValues 
                     |> Seq.concat 
                     |> Seq.sortBy (fun (x,y,z) -> z) 
                     |> Seq.map (fun (x,y,z) -> z) 
                     |> Seq.distinct

Chart.Point (taxicabnumbers,"TaxiCabNumbers","TaxiCab Number")

let taxicabnumbersX = pairValues 
                     |> Seq.concat 
                     |> Seq.sortBy (fun (x,y,z) -> z) 
                     |> Seq.map (fun (x,y,z) -> (x,z)) 
                     

Chart.Point (taxicabnumbersX,"TaxiCabNumbersX","TaxiCab Number in ref to X")

let taxicabnumbersY = pairValues 
                     |> Seq.concat 
                     |> Seq.sortBy (fun (x,y,z) -> z) 
                     |> Seq.map (fun (x,y,z) -> (y,z)) 
                     

Chart.Point (taxicabnumbersY,"TaxiCabNumbersY","TaxiCab Number in ref to Y")


Chart.Combine[
    Chart.Point(taxicabnumbersX, "TaxiCabNumbersX")
    Chart.Point(taxicabnumbersY, "TaxiCabNumbersY")
]

Couldn't fit it in a tweet, so far I have

seq {
    for s in Seq.initInfinite((+)1) do
        let test x y = pown x 3 + pown y 3 = s
        let m = int((float s) ** (1./3.))
        for a in 1..m do
        for b in a+1..m do
        if test a b then
            for c in a+1..m do
            for d in c+1..m do
            if test c d then
                yield s } |> Seq.head

https://twitter.com/fsibot/status/677942849460023296 I did it.